Stability of Slopes(Soil)

Slope are an exposed ground surface that stands at an angle with the horizontal.

Slope is stable (a)if the resistance offered is more than applied force otherwise unstable(b).

Slope & Slope stability of Soil

Types of slope failures

Failures

Translational type

• Failure of slope along weak zone of soil.

• Sliding mass travel long distance before coming to rest.

• Common in coarse grained soil.

Rotational type

• Common in fine grained soils.

• An imaginary axis –point theory exist along which slope is said to rotate to reach a stable position.

• Can be circular & non-circular

Factors effecting slope and stability

Erosion

Water Seepage force

Sudden Drawdown

Earthquakes

Gravity

•Gravity: The universal force that tends to move anything from a high point to a point of equilibrium and additional loads placed on top of the slope increases hence effecting stability.

•Erosion: The wind and flowing water causes erosion of top surface of slope and makes the slope steep and thereby increase the tangential component of driving force.

Contd…..

Contd…•Water Seepage force: Seepage forces in the sloping direction add to gravity forces and make the slope susceptible to instability. The pore water pressure decrease the shear strength. This condition is critical for the downstream slope

•Sudden Drawdown: In this case there is reversal in the direction flow and results in instability of side slope. Due to sudden drawdown the shear stresses are more due to saturated unit weight while the shearing resistance decreases due to pore water pressure that does not dissipate quickly.

Contd…..

•Earthquakes: They induce dynamic shear forces. In addition there is sudden buildup of pore water pressure that reduces available shear strength.

Types of slopes

Slopes

Natural•Hilly & Valley slopes.•River terraces and coastal cliffs.

Man-made

•Embankment for highways and earth dams.•Excavation dumps and waste heaps for landfill.•Landscape development

Illustration of Slopes

Nature of slopes

Slopes

Infinite slopesThey have dimensions that extend over great distances and the soil mass is inclined to the horizontal.

Finite slopesIs one with a base and top surface, the height being limited. The inclined faces of earth dams, embankments and excavation and the like are all finite slopes.

Def: Factor of safety of a slope is defined as the ratio of average shear strength (f ) of a soil to the average shear stress (d) developed along the potential failure surface.

Factor of safety

Contd…The shearing strength mobilized at each point on a failure surface (10.2)

FoS for cohesion and internal friction if different the eq. of mobilsed shearing resistance (10.3)

Example…

Contd…

Stability analysis of slopesInfinite slope (SAND)Assumptions,

β=angle of infinite slope w.r.t horizontal, a cohesion-less soil slope.

Contd…If the slope is stable, slope angle limits to angle of cohesion

FoS of an infinite slope of sand

Infinite slope (CLAY)

Stability analysis of slopes

CONDITION 1:No seepage, no pore pressure.

Vertical stress:

Components of stress:

Value substitution:Allowable height

Contd…

Stability number=

•A dimensionless quantity, is directly proportional to required cohesion an is inversely proportional to allowable height.

Factor of safety,

Critical height

CONDITION 2: (A) Seepage parallel to ground surface

Normal stress:

Shear stress:

Hence, if FoS=1,

Then stability number=

Contd…

Contd…

CONDITION 2: (B) Slope completely submerged under water and no seepage

Stability number=

Where,

example;

Stability analysis of slopesFinite slope

Steps for investigation:

•Assumptions of possible failure surface

•Equilibrium forces acting on the slope.

Methods of Analysis:

Culmann method (Planar failure).

Method considering whole free body: - Slope failure under undrained condition. - Friction-circle method. - Tailor stability number

Method of slice (Swedish c-φ method)

Contd…

Culmann’s Method: for planar failure surface

Assumptions,• failure of a slope occurs along a

plane when the average shearing stress tending to cause the slip is more than the shear strength of the soil.

• Also, the most critical plane is the one that has a minimum ratio of the average shearing stress that tends to cause failure to the shear strength of soil.

Methods of Analysis

Culmann’s Method……

Solving the equations, and substituting&

Types of Rotational (Circular) failure

Face (Slope) failure

Toe failure

Base failure

Face (Slope) failure

• This type of failure occurs when the slope angle (β) is large and when the soil at the toe portion is strong.

Toe failure

• In this case the failure surface passes through the toe. This occurs when the slope is steep and homogeneous.

toe

Base failure

• In this case the failure surface passes below the toe. This generally occurs when the soil below the toe is relatively weak and soft.

Base failed

Failure under undrained conditions (φu=0):

Assumptions,• Soil is homogeneous.• Potential failure surface is a circular arc.• This is seen in fully saturated, undrained soil.

Two failure typesSlope failure

Base failure

Factor of safety

Contd….

Friction-circle method

Contd….Factor of safety using frictional-circle method

Tailor’s stability number:• Taylor (1937) conceived the idea of analyzing the

stability of a large number of slopes through a wide range of slope angles and angles of internal friction, and then representing the results by an abstract number which he called the "stability number".

Stability number

&

Factor of safety

Tailor’s chart:

Fos plot Fφ’ vs Fc’ to find Fs

• In this procedure, the soil above the surface of sliding is divided into a number of vertical parallel slices. The stability of each slice is calculated separately. This is a versatile technique in which the non homogeneity of the soils and pore water pressure can be taken into consideration. It also accounts for the variation of the normal stress along the potential failure surface.

Method of slices:

Method of slices: for steady seepage

Graphical method:

Contd….

Method of slices: Bishop’s method•A simplified and more refined solution.• Useful if slope contains different kind of soil with different C-φ.Here,W = weight of the sliceN = total normal force on the failure surface cdU = pore water pressure = ul on the failure surface cdFR = shear resistance acting on the base of the sliceEr E2 - normal forces on the vertical faces be and adTr T2 = shear forces on the vertical faces be and adθ = the inclination of the failure surface cd to the horizontal

=FoS by conventional method

Where, frictional resistance

And,

Solving and substituting,

Factor of safety

Contd….

Bishop’s and Morgenstern method:

Spencer method:

•Bishop’s method satisfies the equation of equilibrium w.r.t moment but not with force.Factor of safety:

The charts developed by Spencer for different values of Ns, φ'm and ru:

a

b

c

Worked out example:

Thank you